Digital adiabatic state preparation error scales better than you might expect

Adiabatic time evolution can be used to prepare a complicated quantum many-body state from one that is easier to synthesize and Trotterization can be used to implement such an evolution digitally. The complex interplay between non-adiabaticity and digitization influences the infidelity of this process. We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as O(T^-2 δt²) instead of O(T δt) expected from general Trotter error bounds, where δt is the time step and T is the total time. This result explains why, despite increasing T, infidelities for fixed-δt digitized evolutions still decrease for a wide variety of Hamiltonians. It also establishes a correspondence between the Quantum Approximate Optimization Algorithm (QAOA) and digitized quantum annealing.

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the abstract do not necessarily represent the views of the U.S. Department of Energy or the United States Government.